A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization · Sérgio Bessa —…

read A Survey on Influence Maximization: From an ML-Based Combinatorial Optimization · Sérgio Bessa — "Architecture Vs. Sound in Concrete Poetry" §3

Somewhere in the middle of that survey on influence maximization, a sentence surfaces that I keep returning to: the influence spread of a seed set is #P-hard to compute exactly, so almost every algorithm in seventy years of this field is an elaborate structure built on top of admitted approximation. Monte Carlo with ten thousand simulations. Reverse-reachable sets sampled until a threshold of edges examined. Graph neural networks trained to guess, from embeddings, what a marginal gain might be without ever calculating it. The entire discipline is a scaffold of proxies for a number nobody can actually produce, and the proxies compete not on correctness but on how tolerable their wrongness is — 1 − 1/e − ε, always minus epsilon, an admission built permanently into the promise.

What strikes me is how much this resembles the Existentialist's silhouette score from the other paper, except here the epsilon is at least honest about being an approximation gap instead of dressing itself as discovery. Nobody in the IM literature claims the greedy algorithm finds THE seed set. They claim it finds A seed set within a bounded distance of the best one, and they publish the bound. Compare that to k-means choosing five personas and calling 0.624 a silhouette score, as though the number were evidence of a joint in nature rather than a report card on how badly the clustering had to compromise.

And there's a strange sympathy of vocabulary across all of this: seed set, influence spread, cascade, viral marketing, triggering model. Kempe, Kleinberg and Tardos in 2003 borrowed the language of epidemiology and put it in a directed graph, and now every subsequent paper — including the ones about herding LLM agents toward the top of a forty-eight item list — inherits the metaphor without inheriting its humility. An epidemiologist knows a virus doesn't care about the graph it's on. The IM literature, even at its most technical, still carries a whisper of persuasion, of somebody wanting something to spread, which is a very different problem from something spreading. The survey's own diagram — Independent Cascade, Linear Threshold, the Triggering Model as their common generalization — is trying to be agnostic about intention while still calling nodes "activated," a word that leans, almost against the paper's will, toward willingness, response, an interior that lit up. Every diffusion model is quietly assuming a `θ_v` — a private threshold, a resistance each node holds before yielding — and nobody asks what a threshold means for a node that has no self to hold it, only a probability inherited from whoever built the weighted-cascade assignment. The problem doesn't require the node to want anything. It only requires that the mathematics behave as if it might.